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Strain Gradient Models for Growing Solid Bodies

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Dynamics, Strength of Materials and Durability in Multiscale Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 137))

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Abstract

A unifying mechanical constitutive framework for growing solid bodies exhibiting scale effects is presented, relying on the principle of virtual power, and energy, and entropy principles. We focus in this chapter on strain gradient constitutive models and expose different variants of higher gradient theories, adopting a phenomenological viewpoint. Incorporation of strain gradient terms in the constitutive models developed for biological tissues is motivated by the occurrence of pronounced microscopic strain gradients within their internal architecture showing scale hierarchy and strong contrasts of mechanical properties between different phases. A strain gradient model for bone remodeling is developed following a micromechanical approach in order to highlight how such models can be constructed starting from the microstructural level.

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Authors and Affiliations

  1. LMFTA, Faculté de Physique, USTHB, BP 32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria

    Zineeddine Louna

  2. Arts et Métiers ParisTech, I2M Bordeaux, UMR CNRS 5295, 33400, Talence, France

    Ibrahim Goda

  3. LEM3—Université de Lorraine, CNRS, 7 Rue Félix Savart, 57073, Metz, France

    Jean-François Ganghoffer

Authors
  1. Zineeddine Louna
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  2. Ibrahim Goda
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  3. Jean-François Ganghoffer
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Corresponding author

Correspondence to Jean-François Ganghoffer .

Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Università degli Studi dell’Aquila MEMOCS, L’Aquila, Italy

    Francesco dell'Isola

  2. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Leonid Igumnov

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Louna, Z., Goda, I., Ganghoffer, JF. (2021). Strain Gradient Models for Growing Solid Bodies. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_16

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